Should I show that I have a strong work-life balance on my resume? If so, how? If not, why?

Discussing your priorities as they relate to work-life balance is better saved for the interview conversation.  Adding language about your personal preferences on the resume may be misconstrued, and keep you from advancing through the hiring process.  Also, it is important to remember that the resume is about selling yourself to the company and demonstrating that you can do their job.  You are telling them what you have to offer.  It is not a place, necessarily, to discuss your needs and wishes.  However, if you are working through an agency, you may let them know that you are seeking opportunities with flexibility, remote options or even tele-working, so that they can filter opportunities that more directly meet your requirements.

In the interview it is best to listen to the hiring manager’s description of the job and its requirements first - before addressing your specific concerns. Ask other employees about the culture in the company.  Do they offer a flexible work schedule?  Are you able to leave early on occasion?  In this way the company culture and potential work-life options will reveal themselves.  Bringing it up prematurely may, inadvertently, eliminate you as a candidate, under the incorrect assumption that you are not totally interested in their job. 

Asking about vacation time, days off, lunch hours, etc., if they haven’t already been outlined, should be broached once you are sure you are interested in the job and are close to an offer.   When it is clear they want to hire you, you are better able to negotiate the work-life arrangement that is preferable.  Many companies offer work flexibility, which you will likely learn in the first interview.  Additionally, when researching the company, prior to your application or interviews, you may discover information about their work-life balance options.  Again, discuss this in the interview, and not on the resume or cover letter, to better understand whether their objectives coincide with your personal interests.